Descartes'  "Discourse on the Method" 



In his book Discourse on the Method, he attempts to arrive at a fundamental set of principles that one can know as true without any doubt. To achieve this, he employs a method called hyperbolical/metaphysical doubt, also sometimes referred to as methodological skepticism: he rejects any ideas that can be doubted, and then reestablishes them in order to acquire a firm foundation for genuine knowledge. The four principles that he proposed are as follows,

The first was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice.
The second to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.
The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend step by step, to the knowledge of the more complex.
The last, in every case to make enumerations so complete, and reviews s general, that I be assured that nothing was omitted.  

Thus, initially, Descartes arrives at only a single principle: thought exists. Thought cannot be separated from me, therefore, I exist. Most famously, this is known as cogito ergo sum (English: "I think, therefore I am"). Therefore, Descartes concluded, if he doubted, then something or someone must be doing the doubting; therefore the very fact that he doubted proved his existence. "The simple meaning of the phrase is that if one is skeptical of existence that is in and of itself proof that he does exist." 
He perceives his body through the use of the senses; however, these have previously been unreliable. 
To further demonstrate the limitations of the senses, Descartes proceeds with what is known as the Wax Argument. He considers a piece of wax; his senses inform him that it has certain characteristics, such as shape, texture, size, color, smell, and so forth. When he brings the wax towards a flame, these characteristics change completely. However, it seems that it is still the same thing: it is still the same piece of wax, even though the data of the senses inform him that all of its characteristics are different. Therefore, in order to properly grasp the nature of the wax, he should put aside the senses. He must use his mind. 

Descartes' Dreams -

Descartes is often regarded as the first thinker to provide a philosophical framework for the natural sciences as these began to develop.
On the night of 10–11 November 1619, while stationed in Neuburgan der Donau, Germany, Descartes experienced a series of three powerful dreams or visions that he later claimed profoundly influenced his life. In the first of these dreams, Descartes found himself buffeted and thrown down by a powerful whirlwind while walking near a college. In the second, he was awoken by an inexplicable thunder or explosion-like sound in his head to see sparks coming from the stove in his room. In the third dream, he finds a great dictionary and an anthology of ancient Latin poets on his bedside table. In the latter book, he reads a verse that begins, "What path shall I follow in life?" Descartes concluded from these visions that the pursuit of science would prove to be, for him, the pursuit of true wisdom and a central part of his life's work 

Contributions to Mathematics and Physics- 

Descartes' main contribution to the field of Mathematics & Physics were his analytical geometry as well as his theories of vortices respectively. Analytical geometry was no more the application of algebra to geometry. Descartes explains this concept in his book, La Geometrie, published in the year 1637. 

Descartes believed that human efforts were better directed towards the discovery of mechanistic causes of things. Descartes contribution to the field of Physics has made itself evident in the fact that Isaac Newton's first law of motion is based on the principle set forth by Descartes.  

  

Rene Descartes (1596-1650)